Modeling of bounded stochastic processes

Random processes of bounded variation are generated by using of randomized sinusoidal model and nonlinear filter model. In the randomized sinusoidal model, random noises ar\e introduced in phase angles; while in the nonlinear filter model, a set of nonlinear Itô differential equations are employed. In both methods, the spectral density of a modeled random process can be matched by adjusting model parameters. However, the probability density of the process generated by the randomized sinusoidal model has a fixed shape, and cannot be adjusted. On the other hand, the nonlinear filter model covers a variety of profiles of probability distributions.